Moving mesh cosmology: numerical techniques and global statistics

We present the first hydrodynamical simulations of galaxy formation using the new moving
mesh code AREPO and compare the results with equivalent GADGET simulations based on the
traditional smoothed particle hydrodynamics (SPH) technique. Both codes use an identical
Tree-PM gravity solver and include the same sub-resolution physics for the treatment of star
formation, but employ a completely different method to solve the inviscid Euler equations.
This allows us to cleanly assess the impact of hydro-solver uncertainties on the results of
cosmological studies of galaxy formation. In this paper, we focus on predictions for global
baryon statistics, such as the cosmic star formation rate density, after we introduce our simulation
suite and numerical methods. Properties of individual galaxies and haloes are examined
by Keres et al. (2011), while a third paper by Sijacki et al. (2011) uses idealised simulations
to analyse in more detail the differences between the hydrodynamical schemes. We find that
the global baryon statistics differ significantly between the two simulation approaches. AREPO
shows systematically higher star formation rates at late times, lower mean temperatures averaged
over the simulation volume, and different gas mass fractions in characteristic phases
of the intergalactic medium, in particular a reduced amount of hot gas. Although both hydrodynamical
codes use the same implementation of cooling and yield an identical dark matter
halo mass function, more gas cools out of haloes in AREPO compared with GADGET towards
low redshifts, which induces corresponding differences in the late-time star formation rates of
galaxies. We show that this striking difference originates through a higher heating rate with
SPH in the outer parts of haloes, caused by viscous dissipation of SPH's inherent sonic velocity
noise and SPH's efficient damping of subsonic turbulence injected in the halo infall
region, and because of a higher efficiency of gas stripping in AREPO. These differences also
produce more disk-like galaxy morphologies in the moving mesh calculations compared to
SPH. Our results hence demonstrate that inaccuracies in hydrodynamic solvers can lead to
comparatively large systematic differences even at the level of predictions for the global state
of baryons in the universe.

Moving mesh cosmology: the hydrodynamics of galaxy formation

We present a detailed comparison between the well-known smoothed particle
hydrodynamics (SPH) code GADGET and the new moving-mesh code AREPO on a number
of hydrodynamical test problems. Through a variety of numerical experiments with
increasing complexity we establish a clear link between simple test problems with
known analytic solutions and systematic numerical ects seen in cosmological
simulations of galaxy formation. Our tests demonstrate defiencies of the SPH method
in several sectors. These accuracy problems not only manifest themselves in idealized
hydrodynamical tests, but also propagate to more realistic simulation setups of galaxy
formation, ultimately acting local and global gas properties in the full cosmological
framework, as highlighted in companion papers by Vogelsberger et al. (2011) and
Keres et al. (2011). We find that an inadequate treatment of
uid instabilities in
GADGET suppresses entropy generation by mixing, underestimates vorticity generation in
curved shocks and prevents educient gas stripping from infalling substructures.
Moreover, in idealized tests of inside-out disk formation, the convergence rate of gas disk
sizes is much slower in GADGET due to spurious angular momentum transport. In
simulations where we follow the interaction between a forming central disk and
orbiting substructures in a massive halo, the final disk morphology is strikingly dirent
in the two codes. In AREPO, gas from infalling substructures is readily depleted and
incorporated into the host halo atmosphere, facilitating the formation of an extended
central disk. Conversely, gaseous sub-clumps are more coherent in GADGET
simulations, morphologically transforming the central disk as they impact it. The numerical
artefacts of the SPH solver are particularly severe for poorly resolved
ows, and thus
inevitably act cosmological simulations due to their inherently hierarchical nature.
Taken together, our numerical experiments clearly demonstrate that AREPO delivers
a physically more reliable solution.

Moving mesh cosmology: characteristics of galaxies and haloes

We discuss cosmological hydrodynamic simulations of galaxy formation performed with the
new moving-mesh code AREPO, which promises higher accuracy compared with the traditional
SPH technique that has been widely employed for this problem. In this exploratory
study, we deliberately limit the complexity of the physical processes followed by the code for
ease of comparison with previous calculations, and include only cooling of gas with a primordial
composition, heating by a spatially uniform UV background, and a simple sub-resolution
model for regulating star formation in the dense interstellar medium. We use an identical set
of physics in corresponding simulations carried out with the well-tested SPH code GADGET,
adopting also the same high-resolution gravity solver. We are thus able to compare both simulation
sets on an object-by-object basis, allowing us to cleanly isolate the impact of different
hydrodynamical methods on galaxy and halo properties. In accompanying papers, we focus
on an analysis of the global baryonic statistics predicted by the simulation codes (Vogelsberger
et al. 2011), and complementary idealized simulations that highlight the differences
between the hydrodynamical schemes (Sijacki et al. 2011). Here we investigate their influence
on the baryonic properties of simulated galaxies and their surrounding haloes. We find
that AREPO leads to significantly higher star formation rates for galaxies in massive haloes and
to more extended gaseous disks in galaxies, which also feature a thinner and smoother morphology
than their GADGET counterparts. Consequently, galaxies formed in AREPO have larger
sizes and higher specific angular momentum than their SPH correspondents. Interestingly, the
more efficient cooling flows in AREPO yield higher densities and lower entropies in halo centers
compared to GADGET, whereas the opposite trend is found in halo outskirts. The cooling
differences leading to higher star formation rates of massive galaxies in AREPO also slightly
increase the baryon content within the virial radius of massive haloes. We show that these
differences persist as a function of numerical resolution. While both codes agree to acceptable
accuracy on a number of baryonic properties of cosmic structures, our results thus clearly
demonstrate that galaxy formation simulations greatly benefit from the use of more accurate
hydrodynamical techniques such as AREPO and call into question the reliability of galaxy formation
studies in a cosmological context using traditional formulations of SPH. In particular,
our new moving-mesh simulations demonstrate that a population of large disk galaxies can be
formed even without energetic feedback in the form of strong galactic outflows.

Moving mesh cosmology: Properties of Gas Disks

We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the moving-mesh code AREPO. Both codes employ identical gravity solvers and the same sub-resolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic disks. In a matching sample of GADGET and AREPO haloes we fit simulated gas disks with exponential profiles. We find that the cold gas disks formed using AREPO have systematically larger disk scale lengths and higher specific angular momenta than their GADGET counterparts. The reason for these differences is rooted in the inaccuracies of the SPH solver and calls for a reassessment of commonly adopted feedback prescriptions in cosmological simulations.

Moving mesh cosmology: properties of neutral hydrogen in absorption

We examine the distribution of neutral hydrogen in cosmological simulations carried out with the new moving-mesh code AREPO and compare it with the corresponding GADGET simulations based on the smoothed particle hydrodynamics (SPH) technique. The two codes use identical gravity solvers and baryonic physics implementations, but very different methods for solving the Euler equations, allowing us to assess how numerical effects associated with the hydro-solver impact the results of simulations. Here we focus on an analysis of the neutral gas, as detected in quasar absorption lines. We find that the high column density regime probed by Damped Lyman-alpha (DLA) and Lyman Limit Systems (LLS) exhibits significant differences between the codes. GADGET produces spurious artefacts in large halos in the form of gaseous clumps, boosting the LLS cross-section. Furthermore, it forms halos with denser central baryonic cores than AREPO, which leads to a substantially greater DLA cross-section from smaller halos. AREPO thus produces a significantly lower cumulative abundance of DLAs, which is intriguingly in much closer agreement with observations. For the low column density gas probed by the Lyman-alpha forest, the codes differ only at the level of a few percent, suggesting that this regime is quite well described by both methods, a fact that is reassuring for the many Lyman-alpha studies carried out with SPH thus far. While the residual differences are smaller than the errors on current Lyman-alpha forest data, we note that this will likely change for future precision experiments.

Moving mesh cosmology: tracing cosmological gas accretion

We investigate the nature of gas accretion onto haloes and galaxies at z=2 using cosmological hydrodynamic simulations run with the moving mesh code AREPO. Implementing a Monte Carlo tracer particle scheme to determine the origin and thermodynamic history of accreting gas, we make quantitative comparisons to an otherwise identical simulation run with the smoothed particle hydrodynamics (SPH) code GADGET-3.
Contrasting these two numerical approaches, we find significant physical differences in the thermodynamic history of accreted gas in massive haloes above 1010.5 solar masses. In agreement with previous work, GADGET simulations show a cold fraction near unity for galaxies forming in massive haloes, implying that only a small percentage of accreted gas heats to an appreciable fraction of the virial temperature during accretion. The same galaxies in AREPO show a much lower cold fraction, ‹20% in haloes of ~1011 solar masses. This results from a hot gas accretion rate which, at this same halo mass, is an order of magnitude larger than with GADGET, together with a cold accretion rate which is lower by a factor of two. These discrepancies increase for more massive systems, and we explain both trends in terms of numerical inaccuracies with the standard formulation of SPH. We note, however, that changes in the treatment of ISM physics -- feedback, in particular -- could modify the observed differences between codes as well as the relative importance of different accretion modes.
We explore these differences by evaluating several ways of measuring a cold mode of accretion. As in previous work, the maximum past temperature of gas is compared to either a constant threshold value or some fraction of the virial temperature of each parent halo. We find that the relatively sharp transition from cold to hot mode dominated accretion at halo masses of ~1011, is a consequence of the constant temperature criterion, which can only separate virialised gas above some minimum halo mass.
Examining the spatial distribution of accreting gas, we find that the filamentary geometry of accreting gas near the virial radius is a common feature in massive haloes above 1011.5 solar masses. Gas filaments in GADGET, however, tend to remain collimated and flow coherently to small radii, or artificially fragment and form a large number of purely numerical "blobs". These same filamentary gas streams in AREPO show increased heating and disruption at 0.25-0.5 virial radii and contribute to the hot gas accretion rate in a manner distinct from classical cooling flows.